Simplify the following expression: $n = \dfrac{-8t^2}{4t^2 + 2t}$ You can assume $t \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-8t^2 = - (2\cdot2\cdot2 \cdot t \cdot t)$ The denominator can be factored: $4t^2 + 2t = (2\cdot2 \cdot t \cdot t) + (2 \cdot t)$ The greatest common factor of all the terms is $2t$ Factoring out $2t$ gives us: $n = \dfrac{(2t)(-4t)}{(2t)(2t + 1)}$ Dividing both the numerator and denominator by $2t$ gives: $n = \dfrac{-4t}{2t + 1}$